Hi!
The main comparison we can make between Rome and Byzantium is that they had different forms of religion.
The Roman people focused on worshipping Jupiter as a father of all 'gods', while the Byzantium people were just monotheistic.
If you are unaware of the term, monotheistic is basically only believing in and worshipping one and only one god. Polytheistic is the belief in multiple gods.
A similarity between the two empires was that they both gained entertainment from watching gladiator fights!
They often built large structures known as Coliseums in order to hold huge events where the gladiator fights occurred.
Hopefully, this helps! =)